for simultaneously diagonalizable matrices A,B ∈ C . The unbounded drift term is defined by a skew-symmetric matrix S ∈ R. Differential operators of this form appear when investigating rotating waves in time-dependent reaction diffusion systems. As shown in a companion paper, one key assumption to prove resolvent estimates of L∞ in L (R,C ), 1 < p < ∞, is the following L-dissipativity condition...

Consider random matrices A, of dimension m× (m+ n), drawn from an ensemble with probability density f(trAA), with f(x) a given appropriate function. Break A = (B,X) into an m×m block B and the complementary m× n block X , and define the random matrix Z = BX . We calculate the probability density function P (Z) of the random matrix Z and find that it is a universal function, independent of f(x)....

Abstract. We study the density of the roots of the derivative of the characteristic polynomial Z(U, z) of an N × N random unitary matrix with distribution given by Haar measure on the unitary group. Based on previous random matrix theory models of the Riemann zeta function ζ(s), this is expected to be an accurate description for the horizontal distribution of the zeros of ζ (s) to the right of ...

We begin by recalling the core Bayesian hierarchical modeling result of Lindley and Smith (1972), henceforth abbreviated L&S. For n × p1-dimensional response vector z, p1-vector of parameters θ, known n× p1 design matrix A1, and known n× n covariance matrix C1, let the likelihood be z ∼ N(A1θ, C1). Then for second-level p2-vector of parameters μ, known design and covariance matrices A2 and C2, ...

Keywords: Toeplitz matrices Spectral factorization Paraunitary filters Filter design In this work we present the explicit expression of all rectangular Toeplitz matrices B, C which verify the equation BB H + CC H = al for some a > 0. This matrix equation arises in some signal processing problems. For instance, it appears when designing the even and odd components of paraunitary filters, which a...

Introduction This paper is a continuation of [EK3]. In [EK3], we introduced the Hopf algebra F (R) z associated to a quantum R-matrix R(z) with a spectral parameter defined on a 1-dimensional connected algebraic group Σ, and a set of points z = (z 1 , ..., z n) ∈ Σ n. This algebra is generated by entries of a matrix power series T i subject to Faddeev-Reshetikhin-Takhtajan type commutation rela...

The paper is a short survey around the author’s recent works on topics related to complex Monge-Ampère equations and strictly pseudoconvex pseudo-Hermitian manifolds. 1. Invariant differential operators In complex analysis of one variable, the fact that the invariant property for Laplace operator under holomorphic change of coordinates plays an important role. Namely, Let φ : D1 → D2 be a holom...

Abstract. We study the density of the roots of the derivative of the characteristic polynomial Z(U, z) of an N × N random unitary matrix with distribution given by Haar measure on the unitary group. Based on previous random matrix theory models of the Riemann zeta function ζ(s), this is expected to be an accurate description for the horizontal distribution of the zeros of ζ (s) to the right of ...

Abstract— This paper proposes a new type of converter called Single Phase Z-source Matrix Converter (SPZMC). The SPZMC is an ac-to-ac converter device. Simulated using diode bridge bidirectional switch cell. The simulation is performed in different loads with fixed input and variable output frequency. Pulse Width Modulation (PWM) switching strategy is used to obtain the variable frequency. The ...